Chirality

A scale is called chiral if reversing the order of the steps results in a different scale. The two scales form a chiral pair and are right/left-handed. Handedness is determined by writing both scales in their canonical mode and then comparing the size of both. The smallest example of a chiral pair in an EDO is 321/312, with the former being right-handed and the latter being left-handed.

Scales for which this property does not hold are called achiral. For example, the diatonic scale is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.

Properties:

1. Chiral scales can only exist in EDO's larger than 5-EDO
2. Chiral scales are at least max-variety 3 (they cannot be MOS or DE)
3. Chiral scales have at least 3 notes
4. Chiral scales have a density of 1 (see table below)

EDO	Number of Chiral Scales	Percentage of Chiral Scales	Corresponding Ratio
1	0	0.0%	0/1
2	0	0.0%	0/1
3	0	0.0%	0/1
4	0	0.0%	0/1
5	0	0.0%	0/1
6	2	22.2%	2/9
7	4	22.2%	2/9
8	12	40.0%	2/5
9	28	50.0%	1/2
10	60	60.6%	20/33
11	124	66.7%	2/3
12	254	75.8%	254/335
13	504	80.0%	4/5
14	986	84.9%	986/1161
15	1936	88.7%	968/1091
16	3720	91.2%	31/34
17	7200	93.4%	240/257
18	13804	95.0%	493/519
19	26572	96.3%	26/27
20	50892	97.2%	16964/17459